Most importantly, I recommend that other gamers find a community that sees beating games as a basis for having friendly discussion about each game's merits, not as a competition to see who can rack up the biggest list. Though that might be a counterproductive atmosphere to some who seek motivation through competition, it was a great context for me to actually feel like I was making progress.
But you're not in competition with others. Tackling your backlog is about challenging yourself. It is ultimately up to you whether or not to decide if you've "legitimately" beaten a game. Make judgments that you feel you can defend to yourself and feel satisfied with. That said, sites like The Backloggery list various categories of game completion, some of which may be helpful for you if you are on the fence on deciding if you can put a game on your big board.
Feelings of hatred towards the boss is nothing new and have existed since the early of days of mankind. As long as people are forced to do something they do not want to do from a person of greater authority then there will always be this resentment. As such, a spate of boss beating games have appeared in recent months on mobile devices and web alike. I noticed “Beat Your Boss” was high on the Google Play download charts and wanted to find out what the fuss was about.
And even when the game's over, it's not. Beating the game on Normal is a rewarding feat in itself, but that just opens up the hard mode as well as a couple more songs that weren't in the original play through. Getting through that challenge opens up one more track of difficulty. There are more than a dozen and a half songs in Elite Beat Agents, and if you do the math, averaging three minutes of play for each song, there's several hours of single player gaming since there's absolutely no possible way any human could complete this game perfectly in his first sitting. And even when that happens, this Nintendo DS game has a team-based four player competition mode -- if you've got multiple carts you get the whole library of songs that the host has unlocked. For those with only one copy of the game, there's a sampling of songs in Download Play. Either way, multiplayer extends an already great game further than the original Osu! Tatake! Oenden! ever did.